What is the solution set of (x - 2) (x - 3) = 2?

a. {1, 4}

b. {2, 3}

c. {4, 5}

Step One

Remove the brackets. Use Foil

F: x^2

O: - 3x

I: - 2x

L: (-2) (-3) = 6

What you have now is

x^2 - 3x - 2x + 6 = 2

Step Two

Combine like terms.

x^2 - 5x + 6 = 2

Step Three

Subtract 2 from both sides.

x^2 - 5x + 6 - 2 = 0

x^2 - 5x + 4 = 0

Step 4

Factor

(x - 4) (x - 1) = 0

Step 5

Find the zeros.

x - 4 = 0

x = 4

x - 1 = 0

x = 1

Solution Set

(1,4)